Asymptotic behavior of a relativistic diffusion in Robertson-Walker space-times

被引：2

作者：

Angst, Juergen ^{[1
]}

机构：

[1] Univ Rennes 1, IRMAR, Bur 320,Bat 22,Campus Beaulieu, F-35042 Rennes, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 01期

关键词：

Brownian Motion; Relativistic diffusion; Robertson-Walker space-times; Causal boundary; POISSON BOUNDARY; MARKOV-PROCESSES; WORLD-STRUCTURE; CURVATURE; GEOMETRY; POINTS;

D O I：

10.1214/14-AIHP626

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson Walker space time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the causal boundary and we also describe the behavior of the tangent vector in the neighborhood of this limiting point.

引用

页码：376 / 411

页数：36

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